The family were of Huguenot origin, the Bosanquets having fled to England from Lunel, Montpellier in France in 1685 following the revocation of the Edict of Nantes.
Bosanquet was educated at Windlesham House, Eton and King's College, Cambridge, of which he was formerly a Fellow (BA 1860, MA 1863), and was called to the Bar at the Inner Temple in 1863.
With George N. Darby he co-authored A Practical Treatise on the Statutes of Limitations in England and Ireland, his only published work, written in 1867.
On his retirement as Common Serjeant in November 1919 he was succeeded by Henry Fielding Dickens KC.
After her death, he married on 12 August 1885 Philippa Frances, the daughter of William Bence-Jones, with whom he had a son,[6] and other children.